A076704 Numbers k of the form p^q where both p and q are prime and all digits of k are odd.

9, 1331, 357911, 5177717, 5735339, 9393931, 17171515157399, 335571975137771, 7979737131773191, 13337513771953951, 13137917533317175739371379, 33159599371999557199755557, 1593395573971551557179777111133, 131755773357537951113179771515713, 315113377779977515359339551539771

Offset

1,1

Comments

Up to 10^17, there are only 10 odd-digit prime powers of prime numbers. a(1) = 3^2, a(2) = 11^3, a(3) = 71^3, a(4) = 173^3, a(5) = 179^3, a(6) = 211^3, a(7) = 25799^3, a(8) = 69491^3, a(9) = 199831^3, and a(10) = 237151^3.

The only candidates for even-digit prime powers of prime numbers are of the form 2^n, and below 2^10000 there are only 2, 4, 8, 64, and 2048, two of which are not raised to prime powers.

a(11) <= 13137917533317175739371379 and a(12) <= 33159599371999557199755557. - Jinyuan Wang, Mar 02 2020

Links

Giovanni Resta, Table of n, a(n) for n = 1..36 (terms < 10^57)

Mathematica

pp = Sort[ Flatten[ Table[ Prime[n]^Prime[i], {n, 1, PrimePi[ Sqrt[10^17]]}, {i, 1, PrimePi[ Floor[ Log[ Prime[n], 10^17]]]}]]]; Do[ If[ Union[ OddQ[ IntegerDigits[ pp[[n]]]]] == {True}, Print[ pp[[n]]]], {n, 1, Length[pp]}]

Prog

(PARI) lista(nn) = {my(k, v=List([])); forprime(p=2, nn, forprime(q=2, logint(nn, p), if(Set(digits(k=p^q)%2)==[1], listput(v, k)))); Set(v); } \\ Jinyuan Wang, Mar 02 2020

Crossrefs

Cf. A014261, A053810, A075308.

Sequence in context: A020261 A266864 A076442 * A117053 A270067 A213448

Adjacent sequences: A076701 A076702 A076703 * A076705 A076706 A076707

Keyword

nonn,base

Author

Zak Seidov, Oct 26 2002

Extensions

Edited and extended by Robert G. Wilson v, Oct 31 2002

Corrected and edited by Elliott Line, Jul 11 2013

Better definition from Jon E. Schoenfield, Nov 19 2018

Terms a(11) and beyond from Giovanni Resta, Mar 03 2020

Status

approved